The "other cuts" group are those delivered by the local-cuts routine that do not fit into the known classes. We must check each of these 4,482 unknown constraints.

Step 2: Run a reduction procedure that looks for "edge clones." This will reduce the size of some of the unknown constraints (cuts).

Number of cuts: 4482
Number of edge-clone reductions: 597
Number of non-isomorphic cuts: 4482
Writing clone-reduced cuts to cuts.cloned
Completed in 0.21 seconds

Step 3: Run a code to test if some cuts are isomorphic to one another (that is, they have the identical structure but defined on different sets of cities). This can reduce the number of cuts that need to be verified.

Number of cuts: 4482
Number of cuts with no outside node: 0
Number of non-isomorphic cuts: 3923
Writing non-isomorphic cuts to cuts.iso
Completed in 0.23 seconds

We are now down to 3,923 unknown cuts. To verify these we will solve a small TSP for each cut, determining the minimum value a tour can obtain. These values should match the right-hand-side of the inequality.

Step 4: Run Held-Karp on each cut, limiting the number of search nodes to 1,000,000. This is done in parallel, using a boss-worker framework.

Step 10: Time to bring out the big guns. Use Concorde (with local cuts turned off) to solve the remaining 17 TSPs.

Some of these small TSP instances are nasty for Concorde, but they might be easy for other solution methods.
If you want to have a look, this v19.tsp example has only 57 cities any yet gives Concorde (without local cuts) a headache.